The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

This article presents a description of a South African mathematics teacher's struggles to mediate a new national assessment tool called the Common Tasks for Assessment with her grade 9 learners, who are unprepared for the assessment. The purpose of the study is to describe and to identify the constraints on the teacher's mediation attempts. The…